On some measures of noncompactness in the space of continuous functions

Abstract

We consider some quantities in the space of functions continuous on a bounded interval, which are related to monotonicity of functions. Based on those quantities we construct a few measures of noncompactness in the mentioned function space. Several properties of those measures are established; among others it is shown that they are regular or “partly” regular measures and equivalent to the Hausdorff measure of noncompactness.